An embedded circle separates the sphere into two connected components; this is the Jordan curve theorem. A strengthening of this fact, called the Jordan-Schoenflies theorem, says that the two components are disks; i.e. 2,426 more words

## Tags » 3-manifolds

#### A gorgeous but incomplete proof of "The Smale Conjecture"

In 1959 Stephen Smale gave a proof that the group of diffeomorphisms of the 2-sphere has the homotopy-type of the subgroup of linear diffeomorphisms, i.e. the Lie Group O_3. 745 more words